(x-1)*(x+3)=5

Solution for (x-1)*(x+3)=5 equation:

Simplifying
(x + -1)(x + 3) = 5

Reorder the terms:
(-1 + x)(x + 3) = 5

Reorder the terms:
(-1 + x)(3 + x) = 5

Multiply (-1 + x) * (3 + x)
(-1(3 + x) + x(3 + x)) = 5
((3 * -1 + x * -1) + x(3 + x)) = 5
((-3 + -1x) + x(3 + x)) = 5
(-3 + -1x + (3 * x + x * x)) = 5
(-3 + -1x + (3x + x2)) = 5

Combine like terms: -1x + 3x = 2x
(-3 + 2x + x2) = 5

Solving
-3 + 2x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-3 + -5 + 2x + x2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + 2x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + 2x + x2 = 0

Factor a trinomial.
(-4 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}